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There is a slight misunderstanding here. AMD64 refers to the architecture of the processor. As AMD's X86-64 extension prevailed in the "64-Bit format war", it is named after them; just like people used to call all PCs IBM-PC-compatible.

The gist of the matter is: You can install AMD64 software on both AMD and Intel processors, as long as they support that type of architecture (Don't worry, almost all processors released in the last 5 years do). So just go ahead and install Ubuntu using the 64 bit iso.

Finally, if your CPU has PAE enabled, you can access more than the limited "4G" of RAM using 32-bit processors.

The 64-bit instruction set used in both AMD and Intel CPUs now is one that was invented by AMD.

Usually known as "x86-64", it is also known sometimes as "amd64" honoring its AMD heritage, even though it is used universally by both AMD and Intel.

Both AMD and Intel originally invented their own 64-bit instruction sets. Intel's was called IA-64 (brand name "Itanium") and it failed to be successful in the consumer market. The instruction set used by both chipmakers is now the one invented by AMD. One reason AMD's version was successful was that it was backwards-compatible with 32-bit x86 software, so it could run existing operating systems available at the time.

Software vendors usually refer to it as "x86-64" now which is a less confusing term and is actually quite descriptive, because it is a 64-bit extension of the "x86" instruction set. However, the term "amd64" continues to be used by various Linux distributions like Ubuntu.